System and method for forecasting snowfall probability distributions

ABSTRACT

Currently available weather forecasts, which include a specific snowfall accumulation or range, do not convey the probability that snowfall will be within the forecasted snowfall accumulation range, probabilities of other snowfall accumulation amounts, or a forecaster&#39;s level of confidence. A snowfall probability distribution forecasting system is disclosed that uses a rules-based process to leverage third party weather forecasts, including members of ensemble forecasts, to generate snowfall probability distributions forecasting the most likely snowfall accumulation range, the probability that snowfall accumulation will be within the most likely snowfall accumulation range, and probabilities that snowfall accumulation will be outside of the most likely snowfall accumulation range. To ensure consistency with the deterministic forecast, the snowfall probability distribution may be shifted based on a deterministic forecast. Because third party weather forecasts can produce a non-normal distribution of snowfall accumulation forecasts, the snowfall probability distribution may be normalized.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 62/479,062 filed Mar. 30, 2017, the entire contents of which ishereby incorporated by reference.

BACKGROUND

Snowfall accumulation forecasts are of tremendous value to individualsand organizations. Not only do consumers and businesses use snowfallaccumulation forecasts for planning purposes, but transportation systemsand other critical systems components use forecasts of snowfall andother precipitation to adjust operations, prevent damage toinfrastructure, and avoid events that could be hazardous to the public.

Current forecasting methods produce deterministic forecasts forsnowstorms. Those deterministic forecasts include a specific snowfallaccumulation (often a range) at a specific time and place representing abest guess of a meteorologist (or group of meteorologists) makingsubjective determinations based on information from mathematical modelsand the meteorologist's training and experience. Those deterministicforecasts are of tremendous interest, but do not convey additionalinformation such as the probability that snowfall will be within theforecasted snowfall accumulation range and the probabilities of othersnowfall accumulation amounts. Deterministic forecasts also do notconvey a forecaster's level of confidence or how that confidence couldmorph over time.

A probability distribution, rather than a deterministic forecast, wouldconvey a deeper understanding of the broad range of potential outcomesfor each snowstorm and the likelihood of those outcomes.

Modern forecasters have access to dozens of weather forecasts, includingensemble forecasts that use the same mathematical model to performmultiple simulations (called “members”) in an attempt to account for thetwo usual sources of uncertainty in forecast models (errors introducedby the use of imperfect initial conditions and errors introduced becauseof imperfections in the model formulation). No existing weather forecastprovides a probability distribution, for snowfall accumulation orotherwise. Instead, each weather forecast (or member) can be used togenerate a single deterministic forecast.

U.S. Pat. Pub. No. 2014/0303893 to LeBlanc describes a system thatgenerates a probability distribution of snowfall rates by combining aprobability of snowfall with a probability distribution of overallprecipitation rates. However, the LeBlanc system requires bothcalculating the probability of snowfall and generating a probabilitydistribution of overall precipitation rates, which are both difficult todo with precision using existing weather forecasting methods.

Given the desire for a more accurate assessment of the broad range ofpotential outcomes for each snowstorm and the drawbacks of both existingweather forecasts and weather forecasting systems, there is a need for arules-based process to generate snowfall probability distributionsforecasting a plurality of snowfall accumulation ranges and theprobability that snowfall accumulation will be within each of thoseranges. Furthermore, to avoid confusing users, it is important that therules-based process generates snowfall probability distributions thatare consistent with a deterministic forecast for the same location andtime period and reflect a normal distribution from the most likelysnowfall accumulation range to the tails of the probabilitydistribution.

SUMMARY

In order to overcome those and other drawbacks in the prior art, asnowfall probability distribution forecasting system is disclosed thatuses a rules-based process to leverage third party weather forecasts,including members of ensemble forecasts, to generate snowfallprobability distributions forecasting the most likely snowfallaccumulation range, the probability that snowfall accumulation will bewithin the most likely snowfall accumulation range, and probabilitiesthat snowfall accumulation will be outside of the most likely snowfallaccumulation range.

The snowfall probability distribution forecasting system stores aplurality of weather forecasts, identifies a predicted location and apredicted time period of a snowstorm, determines a snowfall accumulationforecast based on each of the plurality of weather forecasts, forms anensemble histogram by identifying a series of consecutive,non-overlapping snowfall accumulation ranges and determining how many ofthe snowfall accumulation forecasts are in each of the snowfallaccumulation ranges, calculates a probability density functionrepresenting the relative likelihood of snowfall accumulation amountsbased on the ensemble histogram, forms a snowfall probabilitydistribution based on the probability density function, generates asnowfall probability forecast (that includes the most likely snowfallaccumulation range and the probability that snowfall accumulation in thepredicted location over the predicted time period will be within themost likely snowfall accumulation range), and outputs the snowfallprobability forecast.

To ensure consistency between a deterministic forecast and the mostlikely snowfall accumulation range indicated by a snowfall probabilitydistribution, the snowfall probability distribution forecasting systemmay shift the snowfall probability distribution so that the forecastedsnowfall accumulation in the deterministic forecast falls within themost likely snowfall accumulation range of the snowfall probabilitydistribution. Furthermore, because third party weather forecasts canproduce a non-normal distribution of snowfall accumulation forecasts,the snowfall probability distribution forecasting system may normalizethe data so that the probabilities of each snowfall accumulation rangedecrease from the most likely snowfall accumulation range of thesnowfall probability distribution to the tails of the snowfallprobability distribution.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of exemplary embodiments may be better understood with referenceto the accompanying drawings, wherein:

FIG. 1 is a diagram illustrating an architecture of a snowfallprobability distribution forecasting system according to an exemplaryembodiment of the present invention;

FIG. 2 is a block diagram illustrating the snowfall probabilitydistribution forecasting system according to an exemplary embodiment ofthe present invention;

FIG. 3 is a flowchart illustrating a process for generating a snowfallprobability distribution according to an exemplary embodiment of thepresent invention;

FIG. 4 is a graph illustrating an example ensemble histogram, an exampleprobability density function, and an example normalized probabilitydensity function;

FIG. 5 is a view output by the graphical user interface that includes asnowfall probability forecast generated using the histogram shown inFIG. 4 according to an exemplary embodiment of the present invention;

FIG. 6 is a view output by the graphical user interface that includes asnowfall probability forecast according to another exemplary embodimentof the present invention;

FIG. 7 is a view output by the graphical user interface that includes asnowfall probability forecast according to another exemplary embodimentof the present invention;

FIG. 8 is a view output by the graphical user interface that includes asnowfall probability forecast according to another exemplary embodimentof the present invention;

FIG. 9 is a view output by the graphical user interface that includes asnowfall probability forecast according to another exemplary embodimentof the present invention; and

FIG. 10 is a view output by the graphical user interface that includes asnowfall probability forecast according to another exemplary embodimentof the present invention.

DETAILED DESCRIPTION

Reference to the drawings illustrating various views of exemplaryembodiments of the present invention is now made. In the drawings andthe description of the drawings herein, certain terminology is used forconvenience only and is not to be taken as limiting the embodiments ofthe present invention. Furthermore, in the drawings and the descriptionbelow, like numerals indicate like elements throughout.

FIG. 1 is a diagram illustrating an architecture 100 of a snowfallprobability distribution forecasting system 200 according to anexemplary embodiment of the present invention.

As shown in FIG. 1, the architecture 100 includes one or more servers120 that receive information from third party data sources 110 andcommunicate with remote client devices 180 via a wide area network 130,such as the internet. The one or more servers 120 may also store data onand read data from non-transitory computer readable storage media 126.The one or more servers 120 may also communicate with one or more localclient devices 140 either directly (via a wired and/or wirelesscommunication path) or via a local area network 132.

The third party data sources 110 may include, for example, serversmaintained by the National Center for Environmental Predictions (NCEPserver 112) and the European Centre for Medium-Range Weather Forecasts(ECMWF server 114). Additional third party data sources 110 may includethe National Weather Service (NWS), the National Hurricane Center (NHC),Environment Canada, other governmental agencies (such as the U.K.Meteorologic Service, the Japan Meteorological Agency, etc.), privatecompanies (such as Vaisalia's U.S. National Lightning Detection Network,Weather Decision Technologies, Inc.), individuals (such as members ofthe Spotter Network), etc.

Each of the one or more servers 120 may be any suitable hardwarecomputing device configured to send and/or receive data via the networks130 and 132. Each of the one or more servers 120 include internalnon-transitory storage media and at least one hardware computerprocessor. The one or more servers 120, may include, for example, anapplication server and a web server that hosts websites accessible toany of the remote client devices 180 that include a web browser.

The non-transitory computer-readable storage media 126 may include harddisks, solid-state memory, etc. The non-transitory computer-readablestorage media 126 may be internal to one of the servers 120 or externalto the one or more servers 120. The one or more servers 120 maycommunicate with the non-transitory computer-readable storage media 126via a wired and/or wireless communication path and/or via the network132.

The networks 130 and 132 may include any combination of the internet,cellular networks, wide area networks (WAN), local area networks (LAN),etc. Communication via the network(s) 130 and 132 may be realized bywired and/or wireless communication paths.

Each of the one or more local client devices 140 may be any suitablehardware computing device configured to send and receive data via thenetwork 132. Each of the one or more local client devices 140 includeinternal non-transitory storage media and at least one hardware computerprocessor. Each of the one or more local client devices 140 may be, forexample, a personal computing device (e.g., a desktop computer, anotebook computer, a tablet, a smartphone, etc.).

Each of the remote client devices 180 may be any suitable hardwarecomputing device configured to receive data via the network 130. Each ofthe remote client devices 180 include internal non-transitory storagemedia and at least one hardware computer processor. The remote clientdevices 180 may include personal computing devices (e.g., desktopcomputers 182, notebook computers, tablets 186, smartphones 184, etc.)that receive and display information received from the network 130 via aweb browser, software applications installed locally or remotely (e.g.,on a server 120), etc. The remote client devices 180 may includesmartphones 184 and/or tablets 186 that receive and display informationreceived from the network 130 via mobile applications, etc. In thesimplest embodiments, the remote client devices 180 receive snowfallprobability distributions generated by the snowfall probabilitydistribution forecasting system 200 and display those snowfallprobability distributions to a user (e.g., via a web browser, mobileapplication, etc.). As will be described in more detail below, theremote client devices 180 may also include other suitable hardwarecomputing devices 188 that receive snowfall probability distributionsgenerated by the snowfall probability distribution forecasting system200 and, in addition to or in lieu of displaying those snowfallprobability distributions to a user, control a hardware or softwaredevice in response to information included in a snowfall probabilitydistribution.

FIG. 2 is a block diagram illustrating the snowfall probabilitydistribution forecasting system 200 according to an exemplary embodimentof the present invention.

As shown in FIG. 2, the snowfall probability distribution forecastingsystem 200 includes a forecast database 240, an analysis unit 260, and agraphical user interface 280. The snowfall probability distributionforecasting system 200 may further include a historical weather database250 and a historical weather forecast database 255.

The forecast database 240 may be any organized collection ofinformation, whether stored on a single tangible device or multipletangible devices (e.g., the non-transitory computer readable storagemedia 126). The forecast database 240 stores third party weatherforecasts 242 received from the third party data sources 110 anddeterministic forecasts 248 generated using the one or more servers 120and/or the one or more local client devices 140. The forecast database240 may also store winter weather messages 246 issued by governmentagencies (e.g., the NWS, local NWS offices, etc.).

The third party weather forecasts 242 are generated using mathematicalmodels of the atmosphere and oceans that forecast future weatherconditions based on estimates of the current weather conditions. Thethird party weather forecasts 242 may include, for example, quantitativeprecipitation forecasts as well as forecasts for temperature, verticalmotion, and relative humidity. The third party weather forecasts 242 maybe ensemble forecasts, which include a number of separate forecasts(called “members”). An ensemble forecast uses the same mathematicalmodel to perform multiple simulations in an attempt to account for thetwo usual sources of uncertainty in forecast models: the errorsintroduced by the use of imperfect initial conditions and errorsintroduced because of imperfections in the model formulation.Accordingly, as used below, the third party weather forecasts 242 refersto each member of an ensemble forecast.

The third party weather forecasts 242 may include, for example, onedeterministic run of the National Centers for Environmental Prediction(NCEP) Global Forecast System (GFS), members (e.g., 20 members) of theGlobal Ensemble Forecast System (GEFS), members (e.g., 26 members) ofthe Storm Prediction Center (SPC) Short Range Ensemble Forecast (SREF),members (e.g., 26 members) of the European Centre for Medium-RangeWeather Forecasts (ECMWF) ensemble prediction system. The NCEP GFSforecast, the GEFS members, and the SREF members may be received fromthe NCEP server 112. The ECMWF members may be received from the ECMWFserver 114.

Winter weather messages 246 are issued by the NWS (and/or local offices)in advance of forecasted winter weather. Winter weather messages includewinter storm warnings, winter storm watches, and winter weatheradvisories.

The deterministic forecasts 248 may also be generated using one or moremathematical models. However, the deterministic forecasts 248 may begenerated or modified by a meteorologist making subjectivedeterminations based on information from those one or more mathematicalmodels and his or her training and experience. A “deterministicforecast” is a prediction of an event of a specific magnitude (or rangeof magnitudes) in a predicted location during a predicted time period(e.g., 8 inches of snowfall in Philadelphia between Mar. 20, 2018, andMar. 22, 2018). The deterministic forecast 248 may be generated by oneor more meteorologists.

The optional historical weather database 250 may be any organizedcollection of information, whether stored on a single tangible device ormultiple tangible devices (e.g., the non-transitory computer readablestorage media 126). The historical weather database 250 may storegeo-located and time-indexed information indicative of past snowfallaccumulations 252.

The optional historical weather forecast database 255 may be anyorganized collection of information, whether stored on a single tangibledevice or multiple tangible devices (e.g., the non-transitory computerreadable storage media 126). The historical weather forecast database255 may store the third party weather forecasts 242 and thedeterministic forecasts 248 for the locations and time periods of thepast snowfall accumulations.

The analysis unit 260 includes a hardware computer processor andsoftware instructions accessible to and executed by the hardwarecomputer processor. The analysis unit 260 may be any suitablecombination of hardware and software configured to receive the thirdparty weather forecasts 242 and deterministic forecasts 248, generatethe snowfall probability distributions based on the third party weatherforecasts 242 and the deterministic forecasts 248 as described in detailbelow, and output those snowfall probability distributions to the remoteclient devices 180. The analysis unit 260 may include, for example, theGrid Analysis and Display System (GrADS)™, which is an interactivedesktop tool that is used for easy access, manipulation, andvisualization of earth science data. The analysis unit may be realized,for example, by one or more servers 120 and/or the remote client devices180 executing software instructions downloaded from the one or moreservers 120.

The graphical user interface 280 may be any interface that outputsinformation (including the snowfall probability distributions discussedbelow) for display to a user. The graphical user interface 280 may begenerated by a web server (e.g., one of the server(s) 120) for displayto users of the remote client devices 180 via web browsers. Additionallyor alternatively, the graphical user interface 280 may be generated bylocal software (e.g., a mobile application) stored on the remote clientdevices 180.

As described above, current forecasting methods produce deterministicforecasts 248 that include a specific snowfall accumulation (often arange) representing a best guess of a meteorologist (or group ofmeteorologists) making subjective determinations based on informationfrom those mathematical models and the meteorologist's training andexperience. Those deterministic forecasts 248, however, do not conveyadditional information such as the probability that snowfall will bewithin the forecasted snowfall accumulation range and the probabilitiesof other snowfall accumulation amounts. As described in detail below,the snowfall probability distribution forecasting system 200 uses arules-based process to leverage third party weather forecasts 242,including members of ensemble forecasts, to generate snowfallprobability distributions forecasting the most likely snowfallaccumulation range, the probability that snowfall accumulation will bewithin the most likely snowfall accumulation range, and probabilitiesthat snowfall accumulation will be outside of the most likely snowfallaccumulation range.

To ensure consistency between a deterministic forecast 248 and the mostlikely snowfall accumulation range indicated by a snowfall probabilitydistribution, the snowfall probability distribution forecasting system200 may shift the snowfall probability distribution so that theforecasted snowfall accumulation in the deterministic forecast 248 fallswithin the most likely snowfall accumulation range of the snowfallprobability distribution. Furthermore, because third party weatherforecasts 242 can produce a non-normal distribution of snowfallaccumulation forecasts, the snowfall probability distributionforecasting system 200 may normalize the data so that the probabilitiesof each snowfall accumulation range decrease from the most likelysnowfall accumulation range of the snowfall probability distribution tothe tails of the snowfall probability distribution.

FIG. 3 is a flowchart illustrating a process 300 for generating asnowfall probability distribution according to an exemplary embodimentof the present invention. The snowfall probability distribution process300 is performed by the analysis unit 260 (e.g., by the server 120).

While the process 300 is described below as generating a snowfallprobability distribution, one of ordinary skill in the art wouldrecognize that a similar process may be used to generate probabilitydistributions of other forecasted weather conditions, including rainfallamount, liquid equivalent amount, ice accumulation, wind speed,temperature, etc.

Third party weather forecasts 242 are received in step 302. The thirdparty weather forecasts 242 may include, for example, a deterministicforecast from the NCEP GFS, 20 members of the GEFS ensemble, 26 membersof the SREF ensemble, and 26 members of the ECMWF ensemble predictionsystem. The NCEP GFS forecast, the GEFS members, and the SREF membersmay be received from the NCEP server 112. The ECMWF members may bereceived from the ECMWF server 114.

Third party weather forecasts 242 are interpolated to conform to auniform geographic grid in step 304.

A snowstorm is identified in step 306. A snowstorm may be identified,for example, when a winter weather message 246 contains a forecastedsnowfall accumulation. Alternatively, a snowstorm may be identified whena deterministic forecast 248 indicates a forecasted snowstorm or amagnitude of forecasted snowfall accumulation.

A predicted location is identified in step 308. The predicted locationmay be, for example, the location identified in the winter weathermessage 246. Alternatively, the predicted location of the snowstorm maybe, for example, the location indicated by the deterministic forecast248 indicating a forecasted snowstorm or a magnitude of forecastedsnowfall accumulation.

A predicted time period is identified in step 310. The predicted timeperiod may be, for example, the time period specified in the winterweather message 246. Alternatively, the predicted time period may be,for example, the forecasted time period of the forecasted snowstorm inthe deterministic forecast 248.

For each third party weather forecast 242, the forecasted snowfallaccumulation in the predicted location during the predicted time periodis determined in step 312. The forecasted snowfall accumulation may bedetermined using the Cobb method, where a snow-to-liquid ratio iscalculated (based on forecasted temperature, forecasted vertical motion,and forecasted relative humidity) and the quantitative precipitationforecast is multiplied by the calculated snow-to-liquid ratio. In someinstances, a third party weather forecast 242 may include classifyingthe precipitation of falling during certain time periods (e.g., as snow,rain, sleet, or mix). In those instances, the forecasted snowfallaccumulation may be determined by outputting the quantitativeprecipitation forecast classified as snow.

A snowfall probability distribution is generated in step 314 based onthe snowfall accumulation forecasts determined in step 312. The snowfallprobability distribution is generated by identifying a series ofconsecutive, non-overlapping snowfall accumulation ranges; forming anensemble histogram by determining how many of the snowfall accumulationforecasts are in each snowfall accumulation range; calculating aprobability density function based on the ensemble histogram; andforming a snowfall probability distribution based on the probabilitydensity function.

The process for generating a snowfall probability distribution isdescribed below with reference to an example scenario where ten thirdparty weather forecasts 242 have snowfall accumulation forecasts for thepredicted location during the predicted time period as follows:

-   -   Member 1: 2 inches    -   Member 2: 1 inch    -   Member 3: 3.5 inches    -   Member 4: 3.5 inches    -   Member 5: 4 inches    -   Member 6: 8 inches    -   Member 7: 7.5 inches    -   Member 8: 2 inches    -   Member 9: 5 inches    -   Member 10: 1 inches

The snowfall accumulation forecasts from the third party weatherforecasts 242 are then binned into the identified snowfall accumulationranges. For example, using 1 inch snowfall accumulation ranges, theexample snowfall accumulation forecasts are binned as follows:

-   -   0-1 inch: 0 (0 percent)    -   1-2 inches: 2 (20 percent)    -   2-3 inches: 2 (20 percent)    -   3-4 inches: 2 (20 percent)    -   4-5 inches: 1 (10 percent)    -   5-6 inches: 1 (10 percent)    -   6-7 inches: 0 (0 percent)    -   7-8 inches: 1 (10 percent)    -   8-9 inches: 1 (10 percent)

The snowfall accumulation ranges may be predetermined. Alternatively,the snowfall accumulation ranges may be identified based on the snowfallaccumulation forecasts. In an exemplary embodiment, five snowfallaccumulation ranges are identified representing the lowest snowfallaccumulation, a low snowfall accumulation, the most likely snowfallaccumulation, a higher snowfall accumulation, and the highest snowfallaccumulation. However, snowfall accumulation may be divided into anynumber of snowfall accumulation ranges. For example, if three snowfallaccumulation ranges are identified, then the example snowfallaccumulation forecasts are binned as follows:

-   -   0-3 inches: 40 percent    -   3-6 inches: 40 percent    -   6-9 inches: 20 percent

In essence, the snowfall probability distribution forecasting system 200generates a snowfall probability distribution where the probability thatforecasted snowfall accumulation in the predicted location during thepredicted time period will be within each snowfall accumulation range isthe percentage of third party weather forecasts 242 with a snowfallaccumulation forecast within each snowfall accumulation range.

The snowfall probability distribution generated in step 314 mayoptionally be shifted based on the deterministic forecast 348 in step316. For example, the original snowfall probability distribution(generated in step 314) may be shifted such that the mode of the shiftedsnowfall probability distribution is equal to the forecasted snowfallaccumulation in the deterministic forecast 348. (The forecasted snowfallaccumulation in the deterministic forecast 348 may be calculated, forexample, using the Cobb method as described above.) The differencebetween the mean of the original snowfall probability distribution andthe shifted snowfall probability distribution is used as a weight toshift every point in the original snowfall probability distribution.Accordingly, the snowfall probability distribution forecasting system200 creates a shifted snowfall probability distribution where the everypoint in the shifted snowfall probability distribution is influenced bythe deterministic forecast 348.

The (original or optionally shifted) snowfall probability distributionmay optionally be normalized in step 318. For example, the snowfallprobability distribution forecasting system 200 may perform an iterativeprocess where data points from the far tails are moved toward the mean(or mode or median) of the probability distribution until theprobabilities of each snowfall accumulation range decrease from the mode(or median or mean) of the snowfall probability distribution to thetails of the snowfall probability distribution.

FIG. 4 is a graph 400 illustrating an example ensemble histogram, anexample probability density function, and an example normalizedprobability density function. (Note that the example illustrated in FIG.4 does not match the example above.)

In the embodiments described above, each third party weather forecast242 is weighted equally when generating the snowfall probabilitydistribution. In other embodiments, however, third party weatherforecasts 242 may be weighted based on their past accuracy forforecasting snowfall accumulation. For example, the snowfall probabilitydistribution forecasting system 200 may use the past snowfallaccumulations 252 and the third party weather forecasts 242 (and,optionally deterministic forecasts 248) for the locations and timeperiods of the snowfall accumulations 252 to construct a statisticalmodel where each of the third party weather forecasts 242 are weightedto form a snowfall probability distribution that most accuratelypredicts the past snowfall accumulations 252. Accordingly, even if theaccuracy of some or all of the third party weather forecasts 242 changesover time (due to changes in climatological conditions or the thirdparty weather forecasts 242), the snowfall probability distributionforecasting system 200 is able to generate snowfall probabilitydistributions that most accurately forecast future snowfallaccumulations.

A snowfall probability forecast is generated in step 320. The snowfallprobability forecast includes the most probable snowfall distributionrange and the probability, based on the snowfall probabilitydistribution, that snowfall accumulation in the predicted locationduring the predicted time period will be within the most likely snowfallaccumulation range. The snowfall probability forecast may also include ahigher snowfall accumulation range (and the probability, based on thesnowfall probability distribution, that snowfall accumulation will bewithin the higher snowfall accumulation range) and a lower snowfallaccumulation range (and the probability, based on the snowfallprobability distribution, that snowfall accumulation will be within thehigher snowfall accumulation range).

The snowfall probability forecast is output in step 322. In the simplestembodiments, the snowfall probability forecast is output to a remoteclient device 180 for display to a user via the graphical user interface280. For example, the snowfall probability forecast may be displayed aspart of a web page or mobile application. In other embodiments, thesnowfall probability forecast may be output to a remote client device180 to control a hardware or software device in response to informationincluded in a snowfall probability forecast. To cite just one example,the snowfall probability forecast may be output to a railway system thatmay be configured to divert or cancel a train route if the probabilityof snow accumulation at or above an accumulation threshold meets orexceeds a probability threshold.

FIG. 5 illustrates a view 500 output by the graphical user interface 280that includes a snowfall probability forecast generated using thehistogram shown in FIG. 4 according to an exemplary embodiment of thepresent invention.

As shown in FIG. 5, the view 500 may include a textual display 550and/or a bar graph 510. The bar graph 510, for example, may include themost likely snowfall accumulation range 515, the probability 525 thatsnowfall accumulation will be within the most likely snowfallaccumulation range 515, and a visual representation 535 of theprobability 525 that snowfall accumulation will be within the mostlikely snowfall accumulation range 515; a higher snowfall accumulationrange 513, the probability 523 that snowfall accumulation will be withinthe higher snowfall accumulation range 513, and a visual representation533 of the probability 523 that snowfall accumulation will be within thehigher snowfall accumulation range 513; a lower snowfall accumulationrange 517, the probability 527 that snowfall accumulation will be withinthe lower snowfall accumulation range 517, and a visual representation537 of the probability 527 that snowfall accumulation will be within thelower snowfall accumulation range 517; the highest snowfall accumulationrange 511, the probability 521 that snowfall accumulation will be withinthe highest snowfall accumulation range 511, and a visual representation531 of the probability 521 that snowfall accumulation will be within thehighest snowfall accumulation range 511; and the lowest snowfallaccumulation range 519, the probability 529 that snowfall accumulationwill be within the lowest snowfall accumulation range 519, and a visualrepresentation 539 of the probability 529 that snowfall accumulationwill be within the lowest snowfall accumulation range 519.

The textual display 550 may include the most likely snowfallaccumulation range 515, the probability 548 that the snowfallaccumulation will be lower than the most likely snowfall accumulationrange 515, and the probability 542 that the snowfall accumulation willbe lower than the most likely snowfall accumulation range 515.

The view 500 may also include the predicted location 552.

FIG. 6 illustrates a view 600 output by the graphical user interface 280that includes a snowfall probability forecast according to anotherexemplary embodiment of the present invention.

As shown in FIG. 6, the view 600 is similar to the view 500 in that itincludes a textual display 550 and a bar graph 510. Additionally, theview 600 includes a line graph 620 illustrating the probabilities (alongthe y-axis) as function of snowfall accumulation (along the x-axis). Theline graph 620 may include a visual representation of the mode, median,and mean of the probability distribution. The line graph 620 may belabeled at certain intervals. For example, as shown in FIG. 6, the linegraph 620 may be labeled along the x-axis at the mean, 1.5 standarddeviations from the mean, and 2.5 standard deviations from the mean.

The graphical user interface 280 may output different views fordifferent users. For example, different views may be output toindividual website visitors, mobile application users, commercial users,government agencies, etc.

FIG. 7 illustrates a view 700 output by the graphical user interface 280that includes a snowfall probability forecast according to anotherexemplary embodiment of the present invention.

As shown in FIG. 7, the view 700 includes the most likely snowfallaccumulation range 715, the probability 725 that snowfall accumulationwill be within the most likely snowfall accumulation range 715, and avisual representation 735 of the probability 725 that snowfallaccumulation will be within the most likely snowfall accumulation range715. The view 700 also includes the probability 728 that snowfallaccumulation will be higher than the most likely snowfall accumulationrange 715 and a visual representation 738 of the probability 728 thatsnowfall accumulation will be higher than the most likely snowfallaccumulation range 715. The view 700 also includes the probability 722that snowfall accumulation will be lower than the most likely snowfallaccumulation range 715 and a visual representation 732 of theprobability 722 that snowfall accumulation will be lower than the mostlikely snowfall accumulation range 715. The view 700 also includes avisual representation 760 of the predicted time period and probabilitiesof various precipitation types during the predicted time period.

FIG. 8 illustrates a view 800 output by the graphical user interface 280that includes a snowfall probability forecast according to anotherexemplary embodiment of the present invention.

As shown in FIG. 8, the view 800 includes the most likely snowfallaccumulation range 815 and a visual representation 845 of the mostlikely snowfall accumulation range 815. The view 800 also includes thehighest accumulation forecast 818 and the lowest accumulation forecast812 as well as a visual representation 842 from the highest accumulationforecast 818 and the lowest accumulation forecast 812. The highestaccumulation forecast 818 may be, for example, the largest snowfallaccumulation forecasted by a single third party forecast 242 and thelowest accumulation forecast 812 may be the smallest snowfallaccumulation forecasted by a single third party forecast 242.Alternatively, the highest accumulation forecast 818 and the lowestaccumulation forecast 812 may be the largest and smallest forecasted bya predetermined number or percentages of third party forecasts 242.

FIG. 9 illustrates a view 900 output by the graphical user interface 280that includes a snowfall probability forecast according to anotherexemplary embodiment of the present invention.

As shown in FIG. 9, the view 900 includes the most likely snowfallaccumulation range 915 and a visual representation 935 of theprobability that snowfall accumulation will be within the most likelysnowfall accumulation range 915. The view 900 also includes a visualrepresentation 938 of the probability that snowfall accumulation will behigher than the most likely snowfall accumulation range 915 and a visualrepresentation 932 of the probability that snowfall accumulation will belower than the most likely snowfall accumulation range 915.

FIG. 10 illustrates a view 1000 output by the graphical user interface280 that includes a snowfall probability forecast according to anotherexemplary embodiment of the present invention.

As shown in FIG. 10, the view 1000 includes the most likely snowfallaccumulation range 1015, the probability 1025 that snowfall accumulationwill be within the most likely snowfall accumulation range 1015, and avisual representation 1035 of the probability 1025 that snowfallaccumulation will be within the most likely snowfall accumulation range1015; a higher snowfall accumulation range 1013, the probability 1023that snowfall accumulation will be within the higher snowfallaccumulation range 1013, and a visual representation 1033 of theprobability 1023 that snowfall accumulation will be within the highersnowfall accumulation range 1013; a lower snowfall accumulation range1017, the probability 1027 that snowfall accumulation will be within thelower snowfall accumulation range 1017, and a visual representation 1037of the probability 1027 that snowfall accumulation will be within thelower snowfall accumulation range 1017; the highest snowfallaccumulation range 1011, the probability 1021 that snowfall accumulationwill be within the highest snowfall accumulation range 1011, and avisual representation 1031 of the probability 1021 that snowfallaccumulation will be within the highest snowfall accumulation range1011; and the lowest snowfall accumulation range 1019, the probability1029 that snowfall accumulation will be within the lowest snowfallaccumulation range 1019, and a visual representation 1039 of theprobability 1029 that snowfall accumulation will be within the lowestsnowfall accumulation range 1019.

While preferred embodiments have been set forth above, those skilled inthe art who have reviewed the present disclosure will readily appreciatethat other embodiments can be realized within the scope of theinvention. Disclosures of specific numbers of hardware components andsoftware modules are illustrative rather than limiting. Accordingly, thepresent invention should be construed as limited only by the appendedclaims.

The invention claimed is:
 1. A method of forecasting snowfallaccumulation, the method comprising: identifying a predicted locationand a predicted time period of a snowstorm; receiving a plurality ofweather forecasts for the predicted time period in the predictedlocation; for each of the plurality of weather forecasts, determining asnowfall accumulation forecast; forming an ensemble histogram byidentifying a series of consecutive, non-overlapping snowfallaccumulation ranges and determining how many of the snowfallaccumulation forecasts are in each of the snowfall accumulation ranges;calculating a probability density function representing the relativelikelihood of snowfall accumulation amounts based on the ensemblehistogram; forming a snowfall probability distribution based on theprobability density function, the snowfall probability distributionincluding: a most likely snowfall accumulation range and a probabilitythat snowfall accumulation in the predicted location over the predictedtime period will be within the most likely snowfall accumulation range;at least one higher snowfall accumulation range and a probability thatsnowfall accumulation in the predicted location over the predicted timeperiod will be within the higher snowfall accumulation range; and atleast one lower snowfall accumulation range and a probability thatsnowfall accumulation in the predicted location over the predicted timeperiod will be within the lower snowfall accumulation range; generatinga snowfall probability forecast that includes the most likely snowfallaccumulation range and the probability that snowfall accumulation in thepredicted location over the predicted time period will be within themost likely snowfall accumulation range; and outputting the snowfallprobability forecast.
 2. The method of claim 1, further comprising:identifying a deterministic snowfall accumulation forecast for thepredicted location over the time period; creating an adjustedprobability density function by: making a mode of the adjustedprobability density function equal to the deterministic snowfallaccumulation forecast; calculating a difference between a mean of theprobability density function and the deterministic snowfall accumulationforecast; and shifting the probability density function based on thedifference between the mean of the probability density function and thedeterministic snowfall accumulation forecast, wherein the snowfallprobability forecast is based on the adjusted probability densityfunction.
 3. The method of claim 1, further comprising: creating anormalized probability density function by moving data points from fartails of the probability density function toward the mean of theprobability density function until the probabilities of each snowfallaccumulation range decrease from the most likely snowfall accumulationrange to the tails of the snowfall probability distribution, wherein thesnowfall probability forecast is based on the normalized probabilitydensity function.
 4. The method of claim 1, wherein the snowfallprobability forecast further includes: the higher snowfall accumulationrange and the probability that snowfall accumulation in the predictedlocation over the predicted time period will be within the highersnowfall accumulation range; and the lower snowfall accumulation rangeand the probability that snowfall accumulation in the predicted locationover the predicted time period will be within the lower snowfallaccumulation range.
 5. The method of claim 4, wherein the snowfallprobability forecast further includes: a highest snowfall accumulationrange and the probability that snowfall accumulation in a predictedlocation over the predicted time period will be within the highestsnowfall accumulation range; and a lowest snowfall accumulation rangeand a probability that snowfall accumulation in the predicted locationover the predicted time period will be within the lowest snowfallaccumulation range.
 6. The method of claim 1, wherein the snowfallaccumulation forecasts are determined based on the plurality of weatherforecasts using a Cobb method.
 7. The method of claim 6, wherein: eachof the plurality of weather forecasts include a forecasted precipitationamount, a forecast forecasted temperature, a forecasted vertical motion,and a forecasted relative humidity; and the snowfall accumulationforecasts are determined by: calculating a snow-to-liquid ratio based onthe forecasted temperature, the forecasted vertical motion, and theforecasted relative humidity; and multiplying the forecast precipitationamount by the snow-to-liquid ratio.
 8. The method of claim 1, whereinthe snowfall probability forecast is output to a remote device fordisplay to a user via a graphical user interface.
 9. The method of claim1, wherein the snowfall probability forecast is output to control aremote device.
 10. The method of claim 1, wherein the plurality ofweather forecasts includes at least one of the National Centers forEnvironmental Prediction (NCEP) Global Forecast System (GFS), one ormore members of the Global Ensemble Forecast System (GEFS), one or moremembers of the NCEP Short Range Ensemble Forecast (SREF), or one or moremembers of the European Centre for Medium-Range Weather (ECMWF)ensemble.
 11. A system, comprising: a forecast database that stores aplurality of weather forecasts; an analysis unit that: identifies apredicted location and a predicted time period of a snowstorm; for eachof the plurality of weather forecasts, determines a snowfallaccumulation forecast; forms an ensemble histogram by identifying aseries of consecutive, non-overlapping snowfall accumulation ranges anddetermining how many of the snowfall accumulation forecasts are in eachof the snowfall accumulation ranges; calculates a probability densityfunction representing the relative likelihood of snowfall accumulationamounts based on the ensemble histogram; forms a snowfall probabilitydistribution based on the probability density function, the snowfallprobability distribution including: a most likely snowfall accumulationrange and a probability that snowfall accumulation in the predictedlocation over the predicted time period will be within the most likelysnowfall accumulation range; at least one higher snowfall accumulationrange and a probability that snowfall accumulation in the predictedlocation over the predicted time period will be within the highersnowfall accumulation range; and at least one lower snowfallaccumulation range and a probability that snowfall accumulation in thepredicted location over the predicted time period will be within thelower snowfall accumulation range; generates a snowfall probabilityforecast that includes the most likely snowfall accumulation range andthe probability that snowfall accumulation in the predicted locationover the predicted time period will be within the most likely snowfallaccumulation range; and outputs the snowfall probability forecast. 12.The system of claim 11, wherein: the forecast database further includesa deterministic snowfall accumulation forecast for the predictedlocation over the time period; and the analysis unit is furtherconfigured to: create an adjusted probability density function by:making a mode of the adjusted probability density function equal to thedeterministic snowfall accumulation forecast; calculating a differencebetween a mean of the probability density function and the deterministicsnowfall accumulation forecast; and shifting the probability densityfunction based on the difference between the mean of the probabilitydensity function and the deterministic snowfall accumulation forecast,wherein the snowfall probability forecast is based on the adjustedprobability density function.
 13. The system of claim 11, wherein theanalysis unit is further configured to: create a normalized probabilitydensity function by moving data points from far tails of the probabilitydensity function toward the mean of the probability density functionuntil the probabilities of each snowfall accumulation range decreasefrom the most likely snowfall accumulation range to the tails of thesnowfall probability distribution, wherein the snowfall probabilityforecast is based on the normalized probability density function. 14.The system of claim 11, wherein the snowfall probability forecastfurther includes: the higher snowfall accumulation range and theprobability that snowfall accumulation in the predicted location overthe predicted time period will be within the higher snowfallaccumulation range; and the lower snowfall accumulation range and theprobability that snowfall accumulation in the predicted location overthe predicted time period will be within the lower snowfall accumulationrange.
 15. The system of claim 14, wherein the snowfall probabilityforecast further includes: a highest snowfall accumulation range and aprobability that snowfall accumulation in the predicted location overthe predicted time period will be within the highest snowfallaccumulation range; and a lowest snowfall accumulation range and aprobability that snowfall accumulation in the predicted location overthe predicted time period will be within the lowest snowfallaccumulation range.
 16. The method of claim 11, wherein the analysisunit is further configured to determine the snowfall accumulationforecasts based on the plurality of weather forecasts using a Cobbmethod.
 17. The method of claim 16, wherein: each of the plurality ofweather forecasts include a forecasted precipitation amount, a forecastforecasted temperature, a forecasted vertical motion, and a forecastedrelative humidity; and the analysis unit is configured to determine thesnowfall accumulation forecasts by: calculating a snow-to-liquid ratiobased on the forecasted temperature, the forecasted vertical motion, andthe forecasted relative humidity; and multiplying the forecastprecipitation amount by the snow-to-liquid ratio.
 18. The method ofclaim 11, wherein the analysis unit outputs the snowfall probabilityforecast to a remote device for display to a user via a graphical userinterface.
 19. The method of claim 11, wherein the analysis unit outputsthe snowfall probability forecast to control a remote device.
 20. Themethod of claim 11, wherein the plurality of weather forecasts includesat least one of the National Centers for Environmental Prediction (NCEP)Global Forecast System (GFS), one or more members of the Global EnsembleForecast System (GEFS), one or more members of the NCEP Short RangeEnsemble Forecast (SREF), or one or more members of the European Centrefor Medium-Range Weather (ECMWF) ensemble.
 21. A non-transitory computerreadable storage medium storing instructions that, when executed by acomputer processor, cause a computing system to: identify a predictedlocation and a predicted time period of a snowstorm; receive a pluralityof weather forecasts for the predicted time period in the predictedlocation; for each of the plurality of weather forecasts, determine asnowfall accumulation forecast; form an ensemble histogram byidentifying a series of consecutive, non-overlapping snowfallaccumulation ranges and determining how many of the snowfallaccumulation forecasts are in each of the snowfall accumulation ranges;calculate a probability density function representing the relativelikelihood of snowfall accumulation amounts based on the ensemblehistogram; form a snowfall probability distribution based on theprobability density function, the snowfall probability distributionincluding: a most likely snowfall accumulation range and a probabilitythat snowfall accumulation in the predicted location over the predictedtime period will be within the most likely snowfall accumulation range;at least one higher snowfall accumulation range and a probability thatsnowfall accumulation in the predicted location over the predicted timeperiod will be within the higher snowfall accumulation range; and atleast one lower snowfall accumulation range and a probability thatsnowfall accumulation in the predicted location over the predicted timeperiod will be within the lower snowfall accumulation range; generate asnowfall probability forecast that includes the most likely snowfallaccumulation range and the probability that snowfall accumulation in thepredicted location over the predicted time period will be within themost likely snowfall accumulation range; and output the snowfallprobability forecast.